Appendix B

Possibility–Probability Transformation

The presentation in this appendix is taken from Flage et al. (2013). Procedures for the transformation from a possibilistic representation to a probabilistic one, and vice versa, have been suggested: see, for example, Dubois et al. (1993). The transformations are not one-to-one, and in going from possibility (probability) to probability (possibility) some information is introduced (lost) in the transformation procedure. However, certain principles can be adopted so that there is minimum loss (introduction) of (artificial) information.

With possibility–probability/probability–possibility transformations, uncertainty propagation can be performed within a single calculus, using Monte Carlo sampling when transforming possibility distributions into probability distributions and fuzzy methods for the converse.

In this appendix we review the possibility–probability transformation method applied in Chapters 8–11 in Part III. Probability–possibility transformation is not considered; we refer to Dubois et al. (1993) for an overview of such methods.

We consider the transformation from a possibility distribution into a probability distribution. The transformation is based on given principles and ensures consistency to the extent that there is no violation of the formal rules connecting probability and possibility when possibility and necessity measures are understood as upper and lower probabilities, and so that the transformation is not arbitrary ...